Wolf-Rayet (WR) stars are evolved massive stars, and the relative number of WC-type and WN-type WRs should vary with the metallicity of the host galaxy, providing a sensitive test of stellar evolutionary theory. However, past studies of the WR content of M31 have been biased toward detecting WC stars, as their emission-line signatures are much stronger than those of WNs. Here, we present the results of a survey covering all of M31's optical disk (2.2deg^2^), with sufficient sensitivity to detect the weaker-lined WN types. We identify 107 newly found WR stars, mostly of WN type. This brings the total number of spectroscopically confirmed WRs in M31 to 154, a number we argue is complete to ~95%, except in regions of unusually high reddening. This number is consistent with what we expect from the integrated H{alpha} luminosity compared to that of M33. The majority of these WRs formed in OB associations around the Population I ring, although 5% are truly isolated. Both the relative number of WC- to WN-type stars as well as the WC subtype distribution suggest that most WRs exist in environments with higher-than-solar metallicities, which is consistent with studies of M31's metallicity. Although the WC to WN ratio we find for M31 is much lower than that found by previous studies, it is still higher than what the Geneva evolutionary models predict. This may suggest that Roche-lobe overflow produces the excess of WC stars observed at high metallicity, or that the assumed rotational velocities in the models are too high.